ATLANTA >> When President-elect Donald Trump takes office in January, Republicans will have the opportunity to pull off something they have wanted to do for years — overhaul Medicaid, the program that provides health care to tens of millions of lower-income and disabled Americans.

Any changes to the $500 billion-plus program hold enormous consequences not only for recipients but also for the states, which share in the cost.

Trump initially said during the presidential campaign that he would not cut Medicaid, but later expressed support for an idea pushed for years by Republicans in Congress — sending a fixed amount of money each year to the states in the form of block grants. Backers say such a change in the Medicaid formula is one of the best ways to rein in spending, but critics say big cuts would follow.

Currently, the federal government pays an agreed-upon percentage of each state’s Medicaid costs, no matter how much they rise in any given year.

Republicans have argued that states have little incentive to keep expenses under control, because no state pays more than half the total cost. Both House Speaker Paul Ryan and Trump’s pick for secretary of health and human services, Georgia Rep. Tom Price, want to switch to block grants.

Key questions facing Republicans will be how the funding is structured and how much flexibility will be given to the states.

“It’s exciting because you know it’s not going to be the same as it was, and it’s nerve-wracking because you know it’s not going to be the same as it was,” said Terry England, a Republican state lawmaker who chairs the House budget committee in Georgia.

Republican control of Congress and the presidency means the GOP can act on its long-held priorities of reining in entitlement programs and repealing President Barack Obama’s health care law, which allowed states to expand the number of people eligible for Medicaid. Thirty-one states have opted for the expansion.

It is not clear what the GOP’s replacement plan will look like. Democrats have warned of dire consequences, and any proposed changes are likely to trigger a fight in Congress.

Last week, the Democratic Governors Association warned that repealing the Affordable Care Act would end health coverage for millions of people and shift the financial burden onto the states, costing them $68.5 billion in uncompensated care over the next decade. The group said the Medicaid expansion alone has provided coverage for millions of Americans who lacked insurance and that it had been a critical tool for states in combating the opioid epidemic.

In 2012, a plan by Ryan to reduce the federal deficit included a proposal to convert Medicaid funding into block grants with a cap on the amount the federal government would provide. Advocacy groups warned that that approach would ultimately lead to fewer people receiving coverage.

The Congressional Budget Office concluded that under Ryan’s proposal, “states would need to increase their spending on these programs, make considerable cutbacks in them, or both.”

Earlier this year, Ryan and Republican leaders offered another, more flexible option: States would receive a fixed amount from Washington for each person enrolled. That approach would allow federal payments to grow if, for example, a recession forced more people onto Medicaid.

More than 70 million are on Medicaid, nearly 10 million of them covered as a result of the expansion.

GOP budget documents say federal spending on Medicaid has increased 200 percent in the past 15 years, and the Congressional Budget Office projects it will climb 68 percent over the next decade to $642 billion. In addition, total state spending on Medicaid is expected to rise from about $216 billion in fiscal year 2015 to more than $337 billion in 2023.

How the GOP overhaul is ultimately structured will be critical, said Matt Salo, executive director of the National Association of Medicaid Directors.

“Some of my members are looking at this and saying if this isn’t done right, if the money doesn’t match what needs to be done, this is potentially the greatest intergovernmental transfer of financial risk in the country’s history,” he said.

States, many of them struggling with budget shortfalls, could end up covering fewer procedures or medications, instituting work requirements or requiring co-pays or premiums. Those that opted to expand Medicaid could decide it’s no longer sustainable.

Among those now covered because of the expansion is 59-year-old Alan Purser of Wynne, Arkansas, who tapped into the program after losing his job in 2014 when the pawnshop where he worked was sold.

A few weeks after signing up, he went to the doctor because of a bad cough. He was diagnosed with blood clots in both lungs and ended up in the hospital for 10 days.

“Honestly, I would be dead without this coverage,” said Purser, who is on disability. “I never would have gone to the doctor without insurance.”

Purser said he fears having his benefits reduced.

“When you live on $730 a month,” he said, “you have to watch where everything goes, and you just can’t start paying more and more for your medicines.”